Question: Simplify the following expression: $ q = \dfrac{5}{9} + \dfrac{-6k - 6}{k + 9} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k + 9}{k + 9}$ $ \dfrac{5}{9} \times \dfrac{k + 9}{k + 9} = \dfrac{5k + 45}{9k + 81} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6k - 6}{k + 9} \times \dfrac{9}{9} = \dfrac{-54k - 54}{9k + 81} $ Therefore $ q = \dfrac{5k + 45}{9k + 81} + \dfrac{-54k - 54}{9k + 81} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{5k + 45 - 54k - 54}{9k + 81} $ $q = \dfrac{-49k - 9}{9k + 81}$